Monday, April 11, 2016

Truncation Selection by 50% (half the population)

Suppose we had a country whose population originally shared the Caucasian average IQ,

(mean = 100; std dev = σ = 15).

And suppose a catastrophe occurred which led to half the population emigrating - such things have been known to happen in European history.

And suppose the brightest were the ones who emigrated.

What would be the average IQ of those who remained?

The proportion who remain, p, is 50%.

From the table at the bottom of the post above, the intensity of selection, i(p) = 0.8

Then use this equation, S = σ * i(p).

The average IQ of those left behind is S = 15 * 0.8 = 12 points below the mean; i.e. the non-emigrating have an average IQ of 88. However, due to regression to the mean, subsequent generations will do better than this.

Their descendants will have an IQ of R = h2S, where h2 = 0.6 (say) is the additive heritability of IQ.

You have to be careful with country IQs. If the country is not ethnically homogeneous you tend to get a stratified society where the average IQ hides more than it illuminates. For example, in Israel the Ashkenazim are smart and tend to dominate at the top of society - but non-Ashkenazim have a more typical Middle-Eastern IQ and numerically dominate - the resulting averaged IQ is documented as 95. Many Latin-American countries are ethnically stratified so one number is not that useful.

If the country has had a dysfunctional economic system and/or history (China is a case in point, Vietnam another), then deprivation will depress IQ scores.